Yeah I think there's a lot of room for experimentation in this area like locking the grid to musical modes (mixylodian, phyrgian), setting up intervals, etc.
Myy experiment kinda supports every mode. For example, you can pick C major scale and it will have exactly the same notes as G Mixolydian or you can pick E Phrygian.
Although, due to the chaotic nature of the simulation and also because the algorithm to pick notes that I chose, there is no tonal center, so strictly speaking we can't determine mode.
https://news.ycombinator.com/item?id=45211868
And AlgoMotion did a pretty popular demonstration of musical cellular automata which I highly recommend giving a watch.
https://www.youtube.com/watch?v=b2SjVwYNr54
A friend of mine just got a LinnStrument and I've been thinking about how cool it would make as a Conway Game of "Music" visualizer.
https://www.rogerlinndesign.com/linnstrument
Very interesting approaches, especially AlgoMotion's. Hudson (author of the first link) doesn't really tell what algorithm exactly do they use.
Although, due to the chaotic nature of the simulation and also because the algorithm to pick notes that I chose, there is no tonal center, so strictly speaking we can't determine mode.